Papers › Classical Limit of genus two DAHA
Classical Limit of genus two DAHA
S. Arthamonov
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We show that one-parameter deformation 𝒜_(q,t) of the skein algebra Sk_q(Σ₂) of a genus two surface suggested in [AS19] is flat. We solve the word problem in the algebra and describe monomial basis. In addition, we calculate the classical limit 𝒜_(q=1,t) of the algebra and prove that it is a one-parameter flat Poisson deformation of the coordinate ring 𝒜_(q=t=1) of an SL(2,ℂ)-charater variety of a genus two surface. As a byproduct, we obtain a remarkably simple presentation in terms of generators and relations for the coordinate ring 𝒜_(q=t=1) of a genus two character variety.
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